How to scale with mirror modifier as if modifier was applied?
Create a new project and remove default cube.
Press Numpad 7 to set Top Orthographic view
Press SHIFT + A, then M, then Y, to add a cylinder



Set Vertices to 8.



Press TAB to enter Edit Mode. Then Press R, and type 22.5



Press ALT + A to deselect all vertices



Drag over the entire shape to select all vertices on top, then press X, then V to delete them.
Press A to select remaining vertices, then I and type .2 to inset 20 cm (default radius should be 1 m)



Press X, then F to delete the inner face



Press CTRL + R, click on the top (in this view) face, then right click to create a loop cut going through the middle of it.



Repeat above step for the right face.



Press A, to select all vertices, hold CTRL, and deselect all vertices in top-right quadrant (including those on edges of the quadrant)



Press X, then V to remove these vertices.



Press TAB, to go back to Object Mode.
Go to Modifier tab, and add a mirror modifier. Add Y to mirrored axes.



Move your mouse over the viewport and press TAB to go to into edit mode again.
Press A to select all vertices, then change Transform Pivot Point from Median Point to 3D Cursor.



If you moved the 3D cursor accidentally, realign it again, by pressing CTRL + S, then W



Press S and scale the shape. It will keep its proportions.